Articles publicats en revistes (Matemàtiques i Informàtica)

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Vascular surgery study of the CGuard MicroNet-covered stent in patients with indication to carotid revascularization: POLGUARD
(Edizioni Minerva Medica, 2023-12-01) Bedkowski, Lukasz; Szkolka, Lukasz; Lyko-Morawska, Dorota; Balocco, Simone; Buczek, Michal; Medon, Ewa; Wolkowski, Maciej; Dryjski, Maciej; Kuczmik, Waclaw
BACKGROUND: In a recent randomized study, MicroNet-covered stent (CGuard) significantly reduced procedural and post-procedural cerebral embolism in relation to a single-layer CREST study carotid stent, but real-life clinical practice data are limited. The aim is to prospectively assess clinical outcomes of CGuard as a routine revascularization tool for patients with indication to carotid revascularization. METHODS: From April 2019 to November 2021, 204 elective patients (age 71.0±7.1years, 69.6% males, 21.7% symptomatic) were enrolled. RESULTS: Mean basal peak-systolic velocity was 251.41±91.85 cm/s with angiographic diameter stenosis 89.7±8.46%. About 34.4% lesions were severely calcified, 6.8% were angulated, and 4.4% showed significant access tortuosity. Access was femoral, with 100% protection device (filter) use. Two hundred and three lesions in 203 patients were treated (1 cross-over to surgery for lack of effective access, no cross-over to other devices); in most cases (66.9%) the stent was placed directly. For pre-dilated lesions, mean balloon diameter was 3.36±0.34mm. Mean nominal stent diameter was 7.64±0.5 mm; length was 37.19±4.5 mm. All stents were post-dilated (balloon diameter 5.2±0.25 mm). Residual stenosis was <30% in all (3.77±6.91%). By discharge, there were 2 minor strokes (0.9%) and one transient ischemic attack. By 30-days, one other minor stroke occurred in relation to de-novo atrial fibrillation. With no deaths or myocardial infarctions, 30-day total death/stroke/myocardial infarction rate was 1.48%. No in-stent thrombosis or patency loss occurred by 30-days. In-stent peak-systolic velocity was 55.49±22.73 cm/s. CONCLUSIONS: Thirty-day results from POLGUARD study indicate safety and a low complication rate of the MicroNet-covered carotid stent use in every-day vascular surgery practice of carotid revascularization. Long-term observation is underway.
Universality for fluctuations of counting statistics of random normal matrices
(London Mathematical Society, 2026-02-16) Marzo Sánchez, Jordi; Molag, Leslie; Ortega Cerdà, Joaquim
We consider the fluctuations of the number of eigenvalues of $n \times n$ random normal matrices depending on a potential $Q$ in a given set $A$. The eigenvalues of random normal matrices are known to form a determinantal point process, and are known to accumulate on a compact set called the droplet under mild conditions on $Q$. When $A$ is a Borel set strictly inside the droplet, we show that the variance of the number of eigenvalues $N_A^{(n)}$ in $A$ has a limiting behavior given by $$ \lim _{n \rightarrow \infty} \frac{1}{\sqrt{n}} \operatorname{Var} N_A^{(n)}=\frac{1}{2 \pi \sqrt{\pi}} \int_{\partial_* A} \sqrt{\Delta Q(z)} d \mathcal{H}^1(z), $$ where $\partial_* A$ is the measure theoretic boundary of $A$, $d H^1(z)$ denotes the one-dimensional Hausdorff measure, and $\Delta=\partial_z \overline{\partial_z}$. We also consider the case where $A$ is a microscopic dilation of the droplet and fully generalize a result by Akemann, Byun, and Ebke for arbitrary potentials. In this result $d \boldsymbol{H}^1(z)$ is replaced by the harmonic measure at $\infty$ associated with the exterior of the droplet. This second result is proved by strengthening results due to Hedenmalm-Wennman and Ameur-Cronvall on the asymptotic behavior of the associated correlation kernel near the droplet boundary.
The signed Varchenko determinant for complexes of oriented matroids.
(Springer Verlag, 2025-03-17) Hochstättler, Winfried; Keip, Sophia; Knauer, Kolja
We generalize the (signed) Varchenko matrix of a hyperplane arrangement to complexes of oriented matroids and show that its determinant has a nice factorization. This extends previous results on hyperplane arrangements and oriented matroids.
On endomorphism universality of sparse graph classes.
(Wiley, 2025-07-01) Knauer, Kolja; Puig i Surroca, G.
We show that every commutative idempotent monoid (a.k.a. lattice) is the endomorphism monoid of a subcubic graph. This solves a problem of Babai and Pultr and the degree bound is best-possible. On the other hand, we show that no class excluding a minor can have all commutative idempotent monoids among its endomorphism monoids. As a by-product, we prove that monoids can be represented by graphs of bounded expansion (reproving a result of Nešetřil and Ossona de Mendez) and $k$-cancellative monoids can be represented by graphs of bounded degree. Finally, we show that not all completely regular monoids can be represented by graphs excluding topological minor (strengthening a result of Babai and Pultr).
Plattenbauten: touching rectangles in space
(Society for Industrial and Applied Mathematics., 2025) Felsner, Stefan; Knauer, Kolja; Ueckerdt, Torsten
Planar bipartite graphs can be represented as touching graphs of horizontal and vertical segments in $\mathbb{R}^2$. We study a generalization in space: touching graphs of axis-aligned rectangles in $\mathbb{R}^3$, and prove that planar 3-colorable graphs can be represented this way. The result implies a characterization of corner polytopes previously obtained by Eppstein and Mumford. A by-product of our proof is a distributive lattice structure on the set of orthogonal surfaces with given skeleton. Further, we study representations by axis-aligned non-coplanar rectangles in $\mathbb{R}^3$ such that all regions are boxes. We show that the resulting graphs correspond to octahedrations of an octahedron. This generalizes the correspondence between planar quadrangulations and families of horizontal and vertical segments in $\mathbb{R}^2$ with the property that all regions are rectangles.
Expected Energy of Zeros of Elliptic Polynomials
(Springer Science + Business Media, 2024-04-12) Torre Estévez, Víctor de la; Marzo Sánchez, Jordi
In 2011, Armentano, Beltrán and Shub obtained a closed expression for the expected logarithmic energy of the random point process on the sphere given by the roots of random elliptic polynomials. We consider a different approach which allows us to extend the study to the Riesz energies and to compute the expected separation distance.
Enhancing point cloud semantic segmentation via scalable domain adaptation with LoRA-enabled PointNet++
(Elsevier, 2026-01-01) Carós, Mariona; Just, Ariadna; Seguí Mesquida, Santi; Vitrià i Marca, Jordi
Semantic segmentation of airborne LiDAR point clouds enables a broad range of urban and environmental applications. However, domain shifts between training and operational data, as well asthefrequentemergenceofnewsemanticclasses,posesignificantchallengesfordeploying deep learning models effectively. In this work, we explore the integration of Low-Rank Adaptation (LoRA), a parameter-efficient fine-tuning technique, into the PointNet++ architecture to address these challenges. We evaluate LoRA in two realistic scenarios: domain adaptation and incremental learning with novel classes, using subsets of large-scale LiDAR datasets under constrained labeled data settings. Our experiments show that LoRA outperforms traditional full f ine-tuning, achieving notable gains (+3.1 IoU for specific classes and +0.3 mIoUonTerLiDAR, +2.7 mIoU on DALES), while exhibiting greater resistance to catastrophic forgetting and improved generalization, particularly for underrepresented classes. Furthermore, LoRA exceeds baseline accuracy with substantially fewer trainable parameters (73.4% reduction), highlighting its suitability for resource-constrained deployment scenarios. We also present TerLiDAR, a publicly available annotated airborne LiDAR dataset covering 51.4 km2 along the Ter River in Catalonia, Spain. It contributes to increasing the diversity of semantic segmentation benchmarks and advancing 3D scene understanding in remote sensing.
Strict rearrangement inequalities: nonexpansivity and periodic Gagliardo semi-norms
(American Mathematical Society (AMS), 2025-07-21) Csató, Gyula; Mas Blesa, Albert
This paper deals with the behavior of the periodic Gagliardo seminorm under two types of rearrangements, namely under a periodic, and respectively a cylindrical, symmetric decreasing rearrangement. Our two main results are Pólya-Szegó type inequalities for these rearrangements. We also deal with the cases of equality. Our method uses, among others, some classical nonexpansivity results for rearrangements for which we provide some slight improvements. Our proof is based on the ideas of [Frank and Seiringer, Non-linear ground state representations and sharp Hardy inequalities, J. Funct. Anal., 2008], where a new proof to deal with the cases of equality in the nonexpansivity theorem was given, albeit in a special case involving the rearrangement of only one function.
Model category structures on truncated multicomplexes for complex geometry
(London Mathematical Society, 2025-11-26) Cirici, Joana; Livernet, Muriel; Whitehouse, Sarah
To a bicomplex one can associate two natural filtrations, the column and row filtrations, and then two associated spectral sequences. This can be generalized to $N$-multicomplexes. We present a family of model category structures on the category of $N$-multicomplexes where the weak equivalences are the morphisms inducing a quasi-isomorphism at a fixed page $r$ of the first spectral sequence and at a fixed page $s$ of the second spectral sequence. Such weak equivalences arise naturally in complex geometry. In particular, the model structures presented here establish a basis for studying homotopy types of almost complex manifolds.
$A_{\infty}$-structures for Bott-Chern and Aeppli cohomologies
(2025-05-07) Cirici, Joana; Garrido Vilallave, Roger; Sopena Gilboy, Anna
In this article, we introduce certain arity-3 operations on complex manifolds arising from homotopy transfer theory. Such operations are related to the triple ABC-Massey products from Bott-Chern to Aeppli cohomology. We present a package for computing such products as well as other cohomological and homotopical invariants for complex nilmanifolds and give some examples.
DeBasher: a flow-based programming bash extension for the implementation of complex and interactive workflows with stateful processes
(BioMed Central, 2025-04-16) Ortiz Martínez, Daniel
Background: Bioinformatics data analysis faces significant challenges. As data analysis often takes the form of pipelines or workflows, workflow managers (WfMs) have become essential. Data flow programming constitutes the preferred approach in WfMs, enabling parallel processes activated reactively based on input availability. While this paradigm typically follows a linear, acyclic progression, cyclic workflows are sometimes necessary in bioinformatics analyses. These cyclic workflows also present an oppor‑ tunity to explore workflow interactivity, a feature not widely implemented in existing WfMs. Results: We propose DeBasher, a tool that adopts the flow‑based programming (FBP) paradigm, in which the workflow components are in control of their life cycle and can store state information, allowing the execution of complex workflows that include cycles. DeBasher also incorporates a powerful model of interactivity, where the user can alter the behavior of a running workflow. Additionally, DeBasher allows the user to define triggers so as to initiate the execution of a complete workflow or a part of it. The ability to execute processes with state and in control of their life cycle also has applications in dynamic scheduling tasks. Furthermore, DeBasher presents a series of extra features, including the combination of multiple workflows at runt‑ ime through a feature we have called runtime piping, switching to static scheduling to increase scalability, or implementing processes in multiple languages. DeBasher has been successfully used to process 131.7 TB of genomic data by means of a variant calling pipeline. Conclusions: DeBasher is an FBP Bash extension that can be useful in a wide range of situations and in particular when implementing complex workflows, workflows with interactivity or triggers, or when a high scalability is required. Keywords: Workflow, Pipeline, Workflow manager, Data flow programming, Flow‑ based programming, Bash, Workflow interactivity, Workflow triggers
Multiple Sampling and Interpolation in a Space of Polynomials
(CRC Press, 2026-01-23) Cruz, Carlos A.; Massaneda Clares, Francesc Xavier; Ortega Cerdà, Joaquim
We study sampling and interpolation arrays with multiplicities for the spaces $\mathcal{P}_k$ of holomorphic polynomials of degree at most $k$. We find that the geometric conditions satisfied by these arrays are in accordance with the conditions satisfied by the sampling and interpolating sequences with unbounded multiplicities in the Fock space, which can be seen as a limiting case of the space $\mathcal{P}_k$ as $k$ tends to infinity. In particular, if the multiplicities tend to infinity, there are no arrays which are simultaneously sampling and interpolating.
Inter-and Intraobserver Variability in Bowel Preparation Scoring for Colon Capsule Endoscopy: Impact of AI-Assisted Assessment Feasibility Study
(MDPI, 2025-08-29) Io Lei, Ian; Gaya, Daniel R.; Robertson, Alexander; Schelde-Olesen, Benedicte; Mapiye, Alice; Bhandare, Anirudh; Lui, Bei Bei; Shekhar, Chander; Valentiner, Ursula; Gilabert Roca, Pere; Laiz Treceño, Pablo; Seguí Mesquida, Santi; Parsons, Nicholas; Huhulea, Cristiana; Wenzek, Hagen; White, Elizabeth; Koulaouzidis, Anastasios; Arasaradnam, Ramesh P.
This study assessed the reliability of AI-assisted bowel cleansing scoring in colon capsule endoscopy using the CC-CLEAR scale. While interobserver agreement was excellent with manual scoring among experienced readers, AI-assisted reads did not improve agreement but showed reduced consistency, particularly among less experienced users. The mean AI-assisted scores were significantly lower than manual scores, highlighting potential interpretive challenges. These findings suggest that AI’s effectiveness currently depends on user expertise, reinforcing the importance of further development and refinement required for a robust AI implementation in CCE.
Periodic solutions to integro-differential equations: variational formulation, symmetry, and regularity
(Taylor & Francis, 2025-01-17) Cabré Vilagut, Xavier; Csató, Gyula; Mas Blesa, Albert
We consider nonconstant periodic constrained minimizers of semilinear elliptic equations for integro-differential operators in $\mathbb{R}$. We prove that, after an appropriate translation, each of them is necessarily an even function which is decreasing in half its period. In particular, it has only two critical points in half its period, the absolute maximum and minimum. If these statements hold for all nonconstant periodic solutions, and not only for constrained minimizers, remains as an open problem. Our results apply to operators with kernels in two different classes: kernels $K$ which are convex and kernels for which $K\left(\tau^{1 / 2}\right)$ is a completely monotonic function of $\tau$. This last new class arose in our previous work on nonlocal Delaunay surfaces in $\mathbb{R}^n$. Due to their symmetry of revolution, it gave rise to a 1d problem involving an operator with a nonconvex kernel. Our proofs are based on a not so well-known Riesz rearrangement inequality on the circle $\mathbb{S}^1$ established in 1976. We also put in evidence a new regularity fact which is a truly nonlocal-semilinear effect and also occurs in the nonperiodic setting. Namely, for nonlinearities in $C^\beta$ and when $2 s+\beta<1$ ( $2 s$ being the order of the operator), the solution is not always $C^{2 s+\beta-\epsilon}$ for all $\epsilon>0$.
On the Arnold Diffusion Mechanism in Medium Earth Orbit
(Springer Verlag, 2024-11-05) Alessi, Elisa Maria; Baldomá Barraca, Inmaculada; Giralt Miron, Mar; Guàrdia Munárriz, Marcel
Space debris mitigation guidelines represent the most effective method to preserve the circumterrestrial environment. Among them, end-of-life disposal solutions play a key role. In this regard, effective strategies should be conceived not only on the basis of novel technologies, but also following an advanced theoretical understanding. A growing effort is devoted to exploit natural perturbations to lead the satellites toward an atmospheric reentry, reducing the disposal cost, also if departing from high-altitude regions. In the case of the Medium Earth Orbit region, home of the navigation satellites (like GPS and Galileo), the main driver is the gravitational perturbation due to the Moon, that can increase the eccentricity in the long term. In this way, the pericenter altitude can get into the atmospheric drag domain and the satellite can eventually reenter. In this work, we show how an Arnold diffusion mechanism can trigger the eccentricity growth. Focusing on the case of Galileo, we consider a hierarchy of Hamiltonian models, assuming that the main perturbations on the motion of the spacecraft are the oblateness of the Earth and the gravitational attraction of the Moon. First, the Moon is assumed to lay on the ecliptic plane and periodic orbits and associated stable and unstable invariant manifolds are computed for various energy levels, in the neighborhood of a given resonance. Along each invariant manifold, the eccentricity increases naturally, achieving its maximum at the first intersection between them. This growth is, however, not sufficient to achieve reentry. By moving to a more realistic model, where the inclination of the Moon is taken into account, the problem becomes non-autonomous and the satellite is able to move along different energy levels. Under the ansatz of transversality of the stable and unstable manifolds in the autonomous case, checked numerically, Poincaré–Melnikov techniques are applied to show how the Arnold diffusion can be attained, by constructing a sequence of homoclinic orbits that connect invariant tori at different energy levels on the normally hyperbolic invariant manifold.
Instanton bundles vs Ulrich bundles on projective spaces
(Springer, 2021-06-01) Costa Farràs, Laura; Miró-Roig, Rosa M. (Rosa Maria)
We relate the existence of rank $r$ Ulrich bundles on a Veronese 3-fold $\left(\mathbb{P}^3, \mathcal{O}_{\mathbb{P}^3}(d)\right)$ with the existence of rank $r$ instanton bundles on $\mathbb{P}^3$. This relation will allow us to prove the existence of rank $r$ Ulrich bundles on $\left(\mathbb{P}^3, \mathcal{O}_{\mathbb{P}^3}(d)\right)$ for certain values of $(d, r)$. For instance, we explicitly determine the integers $r$ such that rank $r$ Ulrich bundles on $\mathbb{P}^3$ for the Veronese embedding $\mathcal{O}_{\mathbb{P}^3}(3)$ exist and, in particular, we solve the first open case of Conjecture 4.1.
Clifford's theorem for coherent systems on surfaces with Kodaira dimension $\kappa \leq 0$
(Springer Nature, 2025-08-21) Costa Farràs, Laura; Macías Tarrío, Irene; Roa-Leguizamón, Leonardo
Let $X$ be a smooth irreducible projective surface with Kodaira dimension $\kappa \leq 0$. The aim of this paper is to establish a version of Clifford's theorem for coherent systems on $X$.
‘t Hooft bundles on the complete flag threefold and moduli spaces of instantons
(Elsevier Masson, 2025-10-01) Antonelli, Vincenzo; Malaspina, Francesco; Marchesi, Simone; Pons Llopis, Joan
In this work we study the moduli spaces of instanton bundles on the flag twistor space $F:=F(0,1,2)$. We stratify them in terms of the minimal twist supporting global sections and we introduce the notion of (special) 't Hooft bundle on $F$. In particular we prove that there exist $\mu$-stable 't Hooft bundles for each admissible charge $k$. We completely describe the geometric structure of the moduli space of (special) 't Hooft bundles for arbitrary charge $k$. Along the way to reach these goals, we describe the possible structures of multiple curves supported on some rational curves in $F$ as well as the family of del Pezzo surfaces realized as hyperplane sections of $F$. Finally we investigate the splitting behavior of 't Hooft bundles when restricted to conics.
Brill-Noether theory of stable vector bundles on ruled surfaces
(Springer Verlag, 2024-05-11) Costa Farràs, Laura; Macías Tarrío, Irene
Let $X$ be a ruled surface over a nonsingular curve $C$ of genus $g \geq 0$. Let $M_H:=M_{X, H}\left(2 ; c_1, c_2\right)$ be the moduli space of $H$-stable rank 2 vector bundles $E$ on $X$ with fixed Chern classes $c_i:=c_i(E)$ for $i=1,2$. The main goal of this paper is to contribute to a better understanding of the geometry of the moduli space $M_H$ in terms of its Brill-Noether locus $W_H^k\left(2 ; c_1, c_2\right)$, whose points correspond to stable vector bundles in $M_H$ having at least $k$ independent sections. We deal with the non-emptiness of this Brill-Noether locus, getting in most of the cases sharp bounds for the values of $k$ such that $W_H^k\left(2 ; c_1, c_2\right)$ is non-empty.
Structural completeness in many-valued logics with rational constants
(University of Notre Dame, 2022-08) Gispert Brasó, Joan; Haniková, Zuzana; Moraschini, Tommaso; Stronkowski, Michal
The logics $\mathbf{R} \mathbf{\L}, \mathbf{R} \mathbf{P}$, and $\mathbf{R G}$ have been obtained by expanding $\{L}$ukasiewicz logic $\mathbf{L}$, product logic $\mathbf{P}$, and Gödel-Dummett logic $\mathbf{G}$ with rational constants. We study the lattices of extensions and structural completeness of these three expansions, obtaining results that stand in contrast to the known situation in $\mathbf{} \mathbf{,} \mathbf{P}$, and $\mathbf{G}$. Namely, $\mathbf{R} \mathbf{L}$ is hereditarily structurally complete. $\mathbf{R} \mathbf{P}$ is algebraized by the variety of rational product algebras that we show to be $\mathcal{Q}$-universal. We provide a base of admissible rules in RP, show their decidability, and characterize passive structural completeness for extensions of $\mathbf{R P}$. Furthermore, structural completeness, hereditary structural completeness, and active structural completeness coincide for extensions of $\mathbf{R P}$, and this is also the case for extensions of RG, where in turn passive structural completeness is characterized by the equivalent algebraic semantics having the joint embedding property. For nontrivial axiomatic extensions of $\mathbf{R G}$ we provide a base of admissible rules. We leave the problem open whether the variety of rational Gödel algebras is $\mathcal{Q}$-universal.

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